MinT - Information on Result #1012019

Information on Result #1012019

Linear OOA(4¹²⁶, 21865, F₄, 3, 19) (dual of [(21865, 3), 65469, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹², 14, F₄, 3, 9) (dual of [(14, 3), 30, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹¹⁴, 21851, F₄, 3, 19) (dual of [(21851, 3), 65439, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹¹⁴, 65553, F₄, 19) (dual of [65553, 65439, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹¹⁴, 65554, F₄, 19) (dual of [65554, 65440, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(4¹¹³, 65537, F₄, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(4⁹⁷, 65537, F₄, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(4¹, 17, F₄, 1) (dual of [17, 16, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹²⁶, 7288, F₄, 21, 19) (dual of [(7288, 21), 152922, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row